Question

Exercise Exercise Respond to the following based on your reading. What is the difference between longitudinal and transverse waves? Compare and contrast the direction of their movement, movement of a molecule through the completion of a cycle, and amplitude and wavelength measurements of each type of wave. Suppose that a wave has a period of 0.03 second. What’s its frequency? Be sure to show the steps for your work. Compare a wave that has a period of 0.03 second with a second wave that has a period of 1⁄4 second. Which wave has the greater frequency? Be sure to show the steps for your work. If a wave has a wavelength of 4.5 meters and a period of 0.007 second, what’s the velocity of the wave? Be sure to show the steps of your work. Using the image below, identify the numbered parts of the wave.

Answer 1

Answer: Waves are periodic disturbance of a medium that transmit carrying energy but not matter.

Depending on which direction the particles oscillate, waves are divided into two types:

- Transverse waves: in these waves, the oscillations occur in a direction perpendicular to the direction of motion of the wave. Examples of transverse waves are the vibrations in a guitar string.

- Longitudinal waves: in these waves, the oscillations occur back and forth along the direction of motion of the wave. Examples of longitudinal waves are sound waves.

As a result, amplitude and wavelength are measured differently in the two types of waves. In particular:

- The amplitude in a transverse wave is measured as the distance between the equilibrium position and the maximum displacement of a particle in the wave, in the direction perpendicular to the motion of the wave. On the other hand, in a longidutinal wave this distance is measured as the maximum displacement along the direction of propagation of the wave.

- The wavelength in a transverse wave is measured as the distance between two consecutive crests (points of maximum displacement) of the wave. For a longitudinal waves, there exist no crests, but regions of highest density of the particles (compressions) and of lowest density of the particles (rarefactions), so the wavelength is measured as the distance between two consecutive regions of compressions (or rarefactions).

Step-by-step explanation:

Answer 2

Transverse waves carry molecules at right angles to the direction in which the wave travels. Within a cycle, molecules move from their normal position to the highest position, back through the normal position to the lowest point, and then back to the normal position. The molecules retain their horizontal positions while vibrating vertically. Amplitude is measured at right angles to the direction of the travel of the wave. Wavelength can be represented as the distance between any two molecules in phase with each other, such as the two nearest molecules at the crests of the wave.

Longitudinal waves carry molecules parallel to the direction in which the wave travels. Within a cycle, a molecule travels in the same direction as the wave (from normal position to its most distant point on one side of its normal position), changes direction, moves back through its normal position to the opposite side of its normal position at a point that corresponds, and then returns to its normal position. The molecules don’t all move at the same time; some remain stationary as others go through a vibrating motion. Compressions and rarefactions occur here. Amplitude is measured parallel to the direction of the wave. Wavelength may be represented as the distance between the two nearest molecules that didn’t vibrate, the two nearest molecules at maximum compression, or the two nearest molecules at maximum rarefaction.

f = 1⁄T

f = 1⁄0.03

f = 33. 3 Hz

The first wave has a frequency of 33.3 Hz:

f1 = 1⁄T1

f1 = 1⁄0.03

f1 = 33. 3 Hz

The second wave has a frequency of 4 Hz. f2 = 1⁄T2

f2 = 1⁄1⁄4

f2 = 1 ÷ 1⁄4

f2 = 1 × 4⁄1

f2 = 1⁄1 × 4⁄1

f2 = 4 Hz

Therefore, the first wave has a higher frequency.

v = I⁄T

v= 4.5⁄0.007

v = 642.9 m/s

Wavelength

Crest

Trough

Amplitude

Step-by-step explanation: